`hati` and `hatj` are unit vectors along x-axis and y-axis respectively what is the magnitude and direction of the vector `hati+hatj` and `hati-hatj` ? What are the magnitudes of components of a vector `veca=2hati+3hatj` along the directions of `hati+hatj and hati-hatj`?

Answer

`sqrt(2),45^(@)` with the x - axis ; `sqrt(2),-45^(@)` with the x - axis , `(5//sqrt(2),-1//sqrt(2))`.